GCSE · Algebraic manipulation

Factorising with common factorsExam-style questions

Why factorising is expansion run backwards, what "factorise fully" demands, and why a difference of two squares splits instantly — plus what the factorised form is actually FOR.

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13 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 1 Level 2 Level 3 Level 4 Level 5

1
Show that $(2n + 1)^2 - (2n - 1)^2$ is a multiple of 8 for every whole number $n$ .
Level 5 · 3 marksTry it
2
Show that $(3n + 2)^2 - (3n - 2)^2$ is a multiple of 24 for every whole number $n$ .
Level 5 · 3 marksTry it